Question: Divide the polynomials.
Solution: Usually, there are many different ways to divide polynomials. Here, we will use the method of splitting the quotient into multiple quotients: $\dfrac{6x^5-2x^4-1}{x}=\dfrac{6x^5}{x}-\dfrac{2x^4}{x}-\dfrac{1}{x}$ Now let's try to cancel common factors in the resulting terms. $\begin{aligned} \dfrac{6x^5}{x}&=6x^4 \\\\ -\dfrac{2x^4}{x}&=-2x^3 \end{aligned}$ $-\dfrac{1}{x}$ doesn't have common factors so it has to stay as it is. In conclusion, this is the result of dividing the polynomials: $6x^4-2x^3-\dfrac{1}{x}$ [I want to see a different way of performing the division.]